1. **State the problem:** We need to estimate the number of gold rings with mass between 1.4 g and 3 g using the histogram data. 2. **Recall the formula for frequency from a histogram:** $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$ 3. **Identify the relevant bars:** - The interval 1.4 g to 3 g spans part of the bar from 1 to 2 g and the entire bar from 2 to 3 g. 4. **Calculate the frequency for the part of the bar from 1 to 2 g that lies between 1.4 and 2 g:** - Height (frequency density) = 25 - Width of full bar = 1 (from 1 to 2) - Width of partial bar = $2 - 1.4 = 0.6$ - Frequency = $25 \times 0.6 = 15$ 5. **Calculate the frequency for the bar from 2 to 3 g:** - Height = 75 - Width = 1 - Frequency = $75 \times 1 = 75$ 6. **Add the two frequencies to estimate total number of rings between 1.4 g and 3 g:** $$15 + 75 = 90$$ 7. **Explain why this is an estimate:** - The histogram assumes uniform distribution of rings within each bar's interval. - Actual masses may not be evenly spread, so the calculated frequency is an approximation. **Final answer:** The estimated number of gold rings with mass between 1.4 g and 3 g is 90.